A targeting methodology is proposed to determine the optimum loads for multiple utilities considering the cost tradeoffs in energy and capital for heat exchanger networks (HENs). The method is based an a newly-developed Cheapest Utility Principle (CUP), which simply states that it is optimal to increase the load of the cheapest utility and maintain the loads of the relatively expensive utilities constant while increasing the total utility consumption. In other words, the temperature driving forces at the utility pinches once optimized do not change even when the minimum approach temperature (Delta T-min) at the process pinch is varied. The CUP holds rigorously when the relationship between the exchanger area and the capital cost is linear. Even when the relationship is non-linear, it proves to be an excellent approximation that reduces the computational effort during multiple utilities targeting. By optimizing the utility pinches sequentially and recognizing that these optimized utility pinches essentially do not change with the process Delta T-min, the results can be elegantly represented through the optimum load distribution (OLD) plots introduced in this work. The total annual cost (TAC) target curves can be then established from the OLD plots for predesign screening of various options that lead to near-minimum cost HENs but involve different combinations of utilities and load distributions. Rather than determine that single value for the global optimum corresponding to the minimum TAG, it is beneficial in practice to define an optimum Delta T-min range because the TAC curves are often reasonably flat in the neighbourhood of the minimum and consequently provide useful flexibility in terms of capital investment.